Energy Flashcards
Define thermal equilibrium.
The energy content and the temperature of the two bodies in contact will no longer be changing with time.
A system in thermal equilibrium having a particular set of macroscopic observables is said to be in a particular __________________.
equilibrium state
A system is in an equilibrium state if macroscopic observable properties have fixed, definite values, independent of “how they got there”. What are these properties called?
Functions of state.
What are some quantities that are not state functions and why?
Work and Heat because both are path dependent.
Give the equation of state of an ideal gas.
PV = NkBT = nmolesRT.
What does the first law of thermodynamics state?
Energy is conserved and heat and work are both forms of energy.
Define internal energy U.
The sum of the energy of all the internal degrees of freedom that the system possesses.
Define degrees of freedom.
Basic Defn: A system variable that’s unbound (free).
Wiki: An independent physical parameter in the formal description of the state of a physical system.
My defintion: A variable that is free to change and describes the system entirely.
True/False:
After the event of delivering energy to the system, you have a way of telling which of Q or W was added (or subtracted from) the system by examing the system’s state.
False.
There is no way of telling.
Give the equation of the change of U, or ΔU, and dU.
ΔU = ΔQ + ΔW.
dU = dQ + dW.
ΔQ, dQ represents heat added to the system.
-ΔQ, -dQ represents heat taken away from the system.
ΔW, dW represents work done to the system.
-ΔW, -dW represents work done by the system.
Give the derivation of work done by compressing a gas for a reversible change.
dW = Fdx = PAdx = -PdV.
The negative sign ensured that the work dW done on the system is positive when dV is negative, i.e. when the gas is being compressed.
Why would more work be required to compress a gas if a piston is not frictionless, or if you move the piston too suddenly and generate shock waves?
Because work is dissipated in the process of each ( you would transform some of the work into heat, or shockwaves).
In general, U = U(T,V) thus a small change in U can be related to changes in T & V by what?
Use the last result to find how adding heat can change the internal energy of gas.
dU = (∂U/∂T)V dT + (∂U/∂V)T dV, by implicit differentiation.
Using dU = dQ - pdV (The 1st Law of Thermodynamics),
dQ/dT = (∂U/∂T)V + [(∂U/∂V)T + P] dV/dT.
What is the amount of heat we have to add to effect a change of temperature under the constraint of keeping the volume constant?
CV = (∂U/∂T)V
What is the amount of heat we have to add to effect a change of temperature under the constraint of keeping pressure constant?
CP = (∂U/∂T)V + [(∂U/∂V)T + P] (∂V/∂T)P
